We investigate electromagnetic radiation from a bunch moving along a corrugated conductive planar structure. The radiation is analyzed at wavelengths which are much greater than the period of the corrugation. In this case, the theoretical solution can be obtained by the use of equivalent boundary conditions (EBC). Here, we consider the case of deep corrugation, i.e. we assume that the depth of the structure is of the same order as an inverse wavenumber. Using the EBC method we obtain the general solution of the problem and investigate it asymptotically. It is shown that the bunch generates surface waves propagating in the plane of the structure, whereas volume radiation is absent at the frequencies under consideration. The surface radiation is analyzed in detail. In particular, it is demonstrated that, under certain conditions, the properties of the surface waves can be used for the determination of the bunch size. In addition, we consider the energy losses of the bunch. Typical dependences of the energy losses on the corrugation parameters are obtained and analyzed.